2x+193=-6/5x+170

Solution for 2x+193=-6/5x+170 equation:

2x+193=-6/5x+170

We move all terms to the left:

2x+193-(-6/5x+170)=0


Domain of the equation: 5x+170)!=0

x∈R


We get rid of parentheses

2x+6/5x-170+193=0

We multiply all the terms by the denominator


2x*5x-170*5x+193*5x+6=0

Wy multiply elements

10x^2-850x+965x+6=0

We add all the numbers together, and all the variables

10x^2+115x+6=0

a = 10; b = 115; c = +6;
Δ = b2-4ac
Δ = 1152-4·10·6
Δ = 12985
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12985}=\sqrt{49*265}=\sqrt{49}*\sqrt{265}=7\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(115)-7\sqrt{265}}{2*10}=\frac{-115-7\sqrt{265}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(115)+7\sqrt{265}}{2*10}=\frac{-115+7\sqrt{265}}{20}
$